使用Python,用numpy和matplotlib实现手写数据优化迭代误差分析,包括(1)网络设置(2)参数训练 (3)绘制图形
时间: 2024-03-08 10:50:51 浏览: 47
好的,我会尽力回答您的问题。首先,为了实现手写数据优化迭代误差分析,我们需要先导入必要的包,包括numpy和matplotlib。以下是导入包的代码:
```python
import numpy as np
import matplotlib.pyplot as plt
```
接下来,我们需要设置神经网络的结构。假设我们的神经网络包含一个输入层、一个隐藏层和一个输出层,其中输入层有784个神经元,隐藏层有64个神经元,输出层有10个神经元。我们可以使用numpy来创建一个包含所有权重和偏差的字典。以下是设置网络的代码:
```python
# 网络设置
input_size = 784
hidden_size = 64
output_size = 10
weights = {
'W1': np.random.randn(input_size, hidden_size),
'b1': np.zeros(hidden_size),
'W2': np.random.randn(hidden_size, output_size),
'b2': np.zeros(output_size)
}
```
在神经网络中,我们需要定义一个代价函数来评估模型的性能。在这里,我们使用交叉熵来作为代价函数。以下是代价函数的代码:
```python
# 代价函数
def cross_entropy_loss(y_pred, y_true):
m = y_pred.shape[0]
p = softmax(y_pred)
log_likelihood = -np.log(p[range(m),y_true])
loss = np.sum(log_likelihood) / m
return loss
```
接下来,我们需要定义前向传播和反向传播函数。前向传播函数将输入数据传递到神经网络中,并计算输出结果。反向传播函数用于计算梯度,并更新权重和偏差。以下是前向传播和反向传播函数的代码:
```python
# 前向传播
def forward_propagation(x, weights):
z1 = np.dot(x, weights['W1']) + weights['b1']
a1 = np.tanh(z1)
z2 = np.dot(a1, weights['W2']) + weights['b2']
return z2
# 反向传播
def backward_propagation(x, y_true, y_pred, weights, learning_rate):
m = x.shape[0]
delta3 = softmax(y_pred)
delta3[range(m), y_true] -= 1
delta2 = np.dot(delta3, weights['W2'].T) * (1 - np.power(np.tanh(np.dot(x, weights['W1']) + weights['b1']), 2))
dW2 = np.dot(np.transpose(np.dot(np.transpose(delta3), np.ones((m,1)))), np.ones((1,m)))
dW1 = np.dot(np.transpose(x), delta2)
db2 = np.sum(delta3, axis=0, keepdims=True)
db1 = np.sum(delta2, axis=0)
weights['W1'] -= learning_rate * dW1
weights['b1'] -= learning_rate * db1
weights['W2'] -= learning_rate * dW2
weights['b2'] -= learning_rate * db2
return weights
```
现在,我们可以训练我们的神经网络了。假设我们有一个包含60000个手写数字的训练集,我们将使用随机梯度下降算法来训练我们的神经网络。以下是训练神经网络的代码:
```python
# 参数训练
def train(x_train, y_train, weights, learning_rate, epochs):
losses = []
for i in range(epochs):
loss = 0.0
for j in range(x_train.shape[0]):
x = x_train[j]
y_true = y_train[j]
y_pred = forward_propagation(x, weights)
loss += cross_entropy_loss(y_pred, y_true)
weights = backward_propagation(x, y_true, y_pred, weights, learning_rate)
losses.append(loss)
print('Epoch', i, 'Loss', loss)
return weights, losses
# 训练数据
weights, losses = train(x_train, y_train, weights, 0.5, 10)
```
最后,我们可以使用matplotlib来绘制误差随时间的变化图。以下是绘制图形的代码:
```python
# 绘制图形
plt.plot(range(len(losses)), losses)
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.show()
```
希望这个代码对您有所帮助!